This invention relates generally to magnetic resonance imaging (MRI), and more particularly, the invention relates to reconstruction of under-sampled k-space trajectories.
MRI signals for reconstructing an image of an object are obtained by placing the object in a magnetic field, applying magnetic gradients for slice selection, applying a magnetic excitation pulse to tilt nuclei spins in the desired slice, and then detecting MRI signals emitted from the tilted nuclei spins while applying readout gradients. The detected signals can be envisioned as traversing lines in a Fourier transformed space (k-space) with the lines aligned and spaced parallel in Cartesian trajectories and emanating from the origin of k-space in spiral trajectories.
A parallel imaging technique, referred to as partially parallel imaging with localized sensitivities or PILS is known for fast imaging using multiple receiver coils. See Griswold et al., xe2x80x9cPartially Parallel Imaging with Localized Sensitivities (PILS),xe2x80x9d Mag Reson Med 44:602-609 (2000) and Madore et al., xe2x80x9cSMASH and SENSE: Experimental and Numerical Comparisons,xe2x80x9d Mag Reson Med 45:1103-1111 (2001), for example. In PILS, imaging time is reduced by encoding for a smaller field of view (FOV) based on a single coil""s region of sensitivity. Data read in from each component coil is separately reconstructed to form a small-FOV image that covers the sensitivity region for each coil. These component images are then pasted together to generate the large-FOV image. The scan is performed by using the same excitation and read out gradients with multiple receiver coils sitting at different locations. The gradients are designed to encode for the size of the FOV covered by the sensitivity region of a single coil. Then, the data from each coil are reconstructed so that each image has the center of the FOV at the center of the sensitivity region of each coil.
With conventional PILS, only one demodulator channel is used for data from all coils. Therefore, the encoding in the readout direction should be designed to cover the full FOV. One reason for this is the use of anti-aliasing filtering after demodulation and before the analog to digital (A/D) conversion. The filtering removes data from one stage that is needed in the next stage. Thus, to enable under-sampling in the readout direction, demodulation must be done sequentially for data from each coil with proper demodulation tailored for each coil. As a result, data acquisition can be less efficient.
Further, when imaging a large FOV, due to the lower limit on the temporal sampling interval, the maximum gradient amplitude is not utilized. Therefore, when imaging a large FOV using PILS, under-sampling in the readout direction, which will allow faster coverage of k-space, is not being exploited. However, if the sampling rate is not high enough to cover the entire FOV of interest in the readout direction, the anti-aliasing filter designed to avoid aliasing for the given sampling rate will filter out signals that are outside of the FOV being encoded. The anti-aliasing filter applied along the spiral readout results in a linear shift-variant response in the image domain. This shift-variant response is illustrated in FIG. 1, which shows the impulse response at four locations. The figure on the left corner shows the four points for which the impulses were applied. The cross-sections of the impulse responses through the center of the impulses parallel to the y axis are plotted in FIG. 1. For signals that are farther away from the center of the FOV, the amplitude is reduced and the response is wider, which results in blurring. This filtering occurs before any processing can be done to increase the FOV using PILS reconstruction.
In accordance with the invention, a separate demodulation channel is provided for each coil in a multi-coil receiver whereby data for all coils are demodulated in parallel. The demodulation for each received signal depends on the center location of sensitivity for each receiver coil. Since an object being off center can be considered as the signal being shifted in the object domain, the data that is collected in the Fourier domain for each coil will have linear phase multiplied to the data that would have been collected without the shift. For a shift amount of (xi, yi, zi) the linear phase multiplied is exe2x88x92i2xcfx80(x,kx+y,ky+z,kz). Therefore, the linear phase is separately unwrapped in the demodulation step for each coil.
The invention object and features thereof will be more readily apparent from the following detailed description and appended claims when taken with the drawings.